On the generalized nyquist stability criterion

Abstract

This paper starts with a straightforward self-contained treatment of the generalized Nyquist stability criterion based on the eigenloci of the open-loop transfer function matrix. The derivation is straightforward and does not invoke algebraic function theory, branch cuts, and Riemann surfaces. A similar criterion is derived for the distributed case where the open-loop transfer function matrices belong to the recently proposed algebra <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B(\sigma_{0})^{m \times m}</tex> [9], [14]. This leads to a new graphical sability test based on eigenloci which applies to distributed, possibly unstable, open-loop transfer functions.